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2017 Qualitative aspects of counting real rational curves on real K3 surfaces
Viatcheslav Kharlamov, Rareş Răsdeaconu
Geom. Topol. 21(1): 585-601 (2017). DOI: 10.2140/gt.2017.21.585


We study qualitative aspects of the Welschinger-like –valued count of real rational curves on primitively polarized real K3 surfaces. In particular, we prove that, with respect to the degree of the polarization, at logarithmic scale, the rate of growth of the number of such real rational curves is, up to a constant factor, the rate of growth of the number of complex rational curves. We indicate a few instances when the lower bound for the number of real rational curves provided by our count is sharp. In addition, we exhibit various congruences between real and complex counts.


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Viatcheslav Kharlamov. Rareş Răsdeaconu. "Qualitative aspects of counting real rational curves on real K3 surfaces." Geom. Topol. 21 (1) 585 - 601, 2017.


Received: 9 June 2015; Revised: 26 January 2016; Accepted: 12 March 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06687813
MathSciNet: MR3608720
Digital Object Identifier: 10.2140/gt.2017.21.585

Primary: 14N99
Secondary: 14J28 , 14P99

Keywords: $K3$ surfaces , real rational curves , Welschinger invariants , Yau–Zaslow formula

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.21 • No. 1 • 2017
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